相干信号的高分辨率测向技术研究
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摘要
随着阵列信号处理理论及其实际应用的快速发展，波达方向估计（DOA：direction of arrival）理论与技术也已经日益成熟。在实际环境中，由于云层、山峰和建筑物等的自然反射影响，以及人为的有意或无意的干扰，相干信号大量存在，对含有不相关信号和相干信号的混合信号进行DOA估计具有重要的现实意义。与不相关信号相比，使用空间谱方法对相干信号进行DOA估计时会直接导致相关矩阵产生秩损，从而使的传统的适用于不相关信号的高分辨率子空间类DOA估计算法失效。目前该领域有许多国内外学者进行研究，试图找到精度更高、计算更简便、阵元利用率更高并且鲁棒性更好的相干信号DOA估计算法。本文对相干信号的DOA估计方法进行了研究，基于矩阵重构法和扩展阵列提出了一些性能优越的有效算法。
1.提出了一种基于额外辅助参考阵元的协方差矩阵重构算法（ABMR：Additional-reference-sensor Based Matrix reconstruction method）。该算法由参考阵元的输出和阵列输出的互协方差构成新的Toeplitz矩阵，阵列中不含有阵元的自相关噪声，适用于非均匀的高斯白噪声环境，同时继承了矩阵重构类算法和传播算子算法计算量小的优点。理论证明了在一维DOA估计中，使用均匀线形阵列（ULA：uniform linear array）时只要入射信号波数小于阵元个数的一半，无论信号是否相干，该算法就可以成功解相干并得到信号波的DOA估计。然后该方法被扩展到二维DOA估计中，分别结合L形阵列（LSA：L-shaped array）和双平行均匀线阵(2PULA：two parallel uniform linear arrays)实现了基于ABMR算法的相干信号DOA估计。
2.分析了阵元间距对测向模糊的影响，结合ABMR算法和扩展阵列，提出了一维线形扩展孔径阵列和二维L形扩展孔径阵列，用相应的低精度DOA估计对周期性模糊的高精度DOA估计的模糊，从而获得高精度无模糊DOA估计，提高了信号入射角估计的精度，并通过了仿真实验结果验证了方法的有效性。
3.提出了一种二维扩展阵型及基于该阵型的解相干算法。该阵型是对传统子阵划分的该进，由标准子阵在迹阵上扩展而成，并将过去没有关注过的迹阵纳入到DOA估计中，提高了二维DOA估计的精度；同时基于二维扩展阵列对传统的矩阵重构法进行改进，使其应用于相干信号的二维DOA估计时具有更大的有效阵列孔径。
4.在传统前向矩阵重构法的基础上引入了后向重构矩阵，联合前向重构矩阵和后向重构矩阵可以构成新的前后向重构矩阵，该矩阵的秩仅与入射信号数目有关，与信号之间的相关度无关。使用前后向重构矩阵获得的有效孔径大于单独使用前向重构矩阵，与前后向平滑方法的阵元利用率相同，但不需要计算整个阵元的协方差矩阵，也不需要平均操作。尽管本章的DOA估计算法是以ULA和URA作为的基础进行推导的，实际上只要可以划分成重叠的中心对称子阵列的阵列都可以运用本章提到的算法。结合ABMR方法可以减少去除噪声的计算量，适用于非均匀白噪声环境的DOA估计。
As the array signal processing theory and the practical application get rapid develop-ment, the theory and technology of direction of arrival(DOA) estimation also have becomemore sophisticated. In the actual environment, because of natural reflections of clouds,mountains and buildings, or the effect of artificial intentionally or unintentionally interfer-ence, there are coherent signal abounding. DOA estimation of mixed signals, which containsnon-corrected signals and coherent signals, has become an important problem. Comparedwith non-coherent signals, coherent signals will cause rank deficiency of the noiseless cor-relation matrix of received signals. Those high-resolution sub-space algorithms for non-coherent signals will fail in this condition. At present, there are many domestic and foreignscholars studying in this field, trying to find a DOA estimation algorithm for coherent sig-nals, which has higher precision, low-complexity calculation, higher sensor utilization andbetter robustness. In this dissertation, the DOA estimation method for coherent signals wasstudied, the basic idea is to rearrange the correlation matrix and expand the array configura-tion.
1. A new covariance matrix reconstruction algorithm based on additional reference sen-sor was proposed. The algorithm constitutes a new Toeplitz matrix with cross covarianceof output of the additional reference sensor and all the other sensors. The reconstructedmatrix does not contain autocorrelation noise, so it is suitable for non-uniform Gaussianwhite noise environment. At the same time, the proposed method has advantages of matrixreconstruction algorithm and the propagator matrix algorithm. It is proven that in the1-Dcondition, the effective array aperture is M/2in an M-dimension ULA. Then we general-ized the proposed method to2-D estimation problems, using the L-shaped array and doubleparallel uniform linear array. The algorithm can successfully estimate the DOA of coherentsignals
2. The dissertation analyze the impact of elements spacing to find angle ambigui-ty. Combining with the ABMR algorithm and extended array, this dissertation proposedone-dimensional linear expanded aperture array and two-dimensional L-shaped expanded aperture array. Low accuracy unambiguous estimation and high accuracy cyclically am-biguous estimation of DOA are obtained from eigenvalue and eigenvector, respectively. Theproposed method uses the low accuracy unambiguous estimation to resolve the ambiguityof the high accuracy cyclically ambiguous estimation. Then high accuracy unambiguous es-timation can be achieved. The simulation results verify the validity of the proposed method.
3. A new method to classify the two-dimensional(2-D) directions of arrival(DOA) es-timation of signals in a coherent environment is proposed. By using the dual-size spreadingarray, which is formed by spreading a sub-array along a trail-array, the correlation matrixcan be rearranged to form a new matrix, whose rank depends on only the number of in-coming waves. This new method can both enlarge the effective aperture and reduce thecomputational complexity of DOA estimation.
4. Besides the traditional forward matrix reconstruction method, backward reconstruc-tion matrix was introduced. By combining the forward rearranged correlation matrix withits conjugated backward form together, it is always possible to estimate any2M/31-DDOAs using M-element ULA and any2(32√2)MN2-D DOAs using M×N-elementURA. The effective aperture is the same as the forward/backward spatial smoothingmethod, which is greater than the traditional reconstruction matrix. The proposed methodcould both enlarge the effective aperture and reduce the computational complexity.
1.提出了一种基于额外辅助参考阵元的协方差矩阵重构算法（ABMR：Additional-reference-sensor Based Matrix reconstruction method）。该算法由参考阵元的输出和阵列输出的互协方差构成新的Toeplitz矩阵，阵列中不含有阵元的自相关噪声，适用于非均匀的高斯白噪声环境，同时继承了矩阵重构类算法和传播算子算法计算量小的优点。理论证明了在一维DOA估计中，使用均匀线形阵列（ULA：uniform linear array）时只要入射信号波数小于阵元个数的一半，无论信号是否相干，该算法就可以成功解相干并得到信号波的DOA估计。然后该方法被扩展到二维DOA估计中，分别结合L形阵列（LSA：L-shaped array）和双平行均匀线阵(2PULA：two parallel uniform linear arrays)实现了基于ABMR算法的相干信号DOA估计。
2.分析了阵元间距对测向模糊的影响，结合ABMR算法和扩展阵列，提出了一维线形扩展孔径阵列和二维L形扩展孔径阵列，用相应的低精度DOA估计对周期性模糊的高精度DOA估计的模糊，从而获得高精度无模糊DOA估计，提高了信号入射角估计的精度，并通过了仿真实验结果验证了方法的有效性。
3.提出了一种二维扩展阵型及基于该阵型的解相干算法。该阵型是对传统子阵划分的该进，由标准子阵在迹阵上扩展而成，并将过去没有关注过的迹阵纳入到DOA估计中，提高了二维DOA估计的精度；同时基于二维扩展阵列对传统的矩阵重构法进行改进，使其应用于相干信号的二维DOA估计时具有更大的有效阵列孔径。
4.在传统前向矩阵重构法的基础上引入了后向重构矩阵，联合前向重构矩阵和后向重构矩阵可以构成新的前后向重构矩阵，该矩阵的秩仅与入射信号数目有关，与信号之间的相关度无关。使用前后向重构矩阵获得的有效孔径大于单独使用前向重构矩阵，与前后向平滑方法的阵元利用率相同，但不需要计算整个阵元的协方差矩阵，也不需要平均操作。尽管本章的DOA估计算法是以ULA和URA作为的基础进行推导的，实际上只要可以划分成重叠的中心对称子阵列的阵列都可以运用本章提到的算法。结合ABMR方法可以减少去除噪声的计算量，适用于非均匀白噪声环境的DOA估计。
As the array signal processing theory and the practical application get rapid develop-ment, the theory and technology of direction of arrival(DOA) estimation also have becomemore sophisticated. In the actual environment, because of natural reflections of clouds,mountains and buildings, or the effect of artificial intentionally or unintentionally interfer-ence, there are coherent signal abounding. DOA estimation of mixed signals, which containsnon-corrected signals and coherent signals, has become an important problem. Comparedwith non-coherent signals, coherent signals will cause rank deficiency of the noiseless cor-relation matrix of received signals. Those high-resolution sub-space algorithms for non-coherent signals will fail in this condition. At present, there are many domestic and foreignscholars studying in this field, trying to find a DOA estimation algorithm for coherent sig-nals, which has higher precision, low-complexity calculation, higher sensor utilization andbetter robustness. In this dissertation, the DOA estimation method for coherent signals wasstudied, the basic idea is to rearrange the correlation matrix and expand the array configura-tion.
1. A new covariance matrix reconstruction algorithm based on additional reference sen-sor was proposed. The algorithm constitutes a new Toeplitz matrix with cross covarianceof output of the additional reference sensor and all the other sensors. The reconstructedmatrix does not contain autocorrelation noise, so it is suitable for non-uniform Gaussianwhite noise environment. At the same time, the proposed method has advantages of matrixreconstruction algorithm and the propagator matrix algorithm. It is proven that in the1-Dcondition, the effective array aperture is M/2in an M-dimension ULA. Then we general-ized the proposed method to2-D estimation problems, using the L-shaped array and doubleparallel uniform linear array. The algorithm can successfully estimate the DOA of coherentsignals
2. The dissertation analyze the impact of elements spacing to find angle ambigui-ty. Combining with the ABMR algorithm and extended array, this dissertation proposedone-dimensional linear expanded aperture array and two-dimensional L-shaped expanded aperture array. Low accuracy unambiguous estimation and high accuracy cyclically am-biguous estimation of DOA are obtained from eigenvalue and eigenvector, respectively. Theproposed method uses the low accuracy unambiguous estimation to resolve the ambiguityof the high accuracy cyclically ambiguous estimation. Then high accuracy unambiguous es-timation can be achieved. The simulation results verify the validity of the proposed method.
3. A new method to classify the two-dimensional(2-D) directions of arrival(DOA) es-timation of signals in a coherent environment is proposed. By using the dual-size spreadingarray, which is formed by spreading a sub-array along a trail-array, the correlation matrixcan be rearranged to form a new matrix, whose rank depends on only the number of in-coming waves. This new method can both enlarge the effective aperture and reduce thecomputational complexity of DOA estimation.
4. Besides the traditional forward matrix reconstruction method, backward reconstruc-tion matrix was introduced. By combining the forward rearranged correlation matrix withits conjugated backward form together, it is always possible to estimate any2M/31-DDOAs using M-element ULA and any2(32√2)MN2-D DOAs using M×N-elementURA. The effective aperture is the same as the forward/backward spatial smoothingmethod, which is greater than the traditional reconstruction matrix. The proposed methodcould both enlarge the effective aperture and reduce the computational complexity.
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